Large-$S$ limit of the large-$N$ theory for the triangular antiferromagnet

Abstract

Large-$S$ and large-$N$ theories (spin value $S$ and spinor component number $N$) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-$S$ spin-wave theory captures the correct semiclassical behavior, large-$N$ theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the non-trivial recovery of the semiclassical magnetic excitations within a large-$N$ approach, we compute the large-$S$ limit of the dynamic spin structure of the triangular lattice Heisenberg antiferromagnet within a Schwinger boson spin representation. We demonstrate that, only after the incorporation of Gaussian ($1/N$) corrections to the saddle-point ($N=\infty$) approximation, we are able to exactly reproduce the linear spin wave theory results in the large-$S$ limit. The key observation is that the effect of $1/N$ corrections is to cancel out exactly the main contribution of the saddle-point solution; while the collective modes (magnons) consist of two spinon bound states arising from the poles of the RPA propagator. This result implies that it is essential to consider the interaction of the spinons with the emergent gauge fields and that the magnon dispersion relation should not be identified with that of the saddle-point spinons.

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• Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets
• Evidence of Two-Spinon Bound States in the Magnetic Spectrum of Ba${}_3$CoSb${}_2$O${}_9$
• Schwinger boson theory of ordered magnets
• Decay and renormalization of a longitudinal mode in a quasi-two-dimensional antiferromagnet
• Probing magnetism in moiré heterostructures with quantum twisting microscopes
• Interplay between spatial anisotropy and further exchange interactions in the triangular Heisenberg model
• Theoretical analysis of FMR-driven spin pumping current and its properties via Self-Consistent Harmonic Approximation
• Why the Schwinger Boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?
• Field-driven transition from quantum spin liquid to magnetic order in triangular-lattice antiferromagnets
• Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• From deconfined spinons to coherent magnons in an antiferromagnetic Heisenberg chain with long range interactions